# Static general relativistic solutions supported by phantom and ordinary scalar fields with higher-order potentials

## TL;DR

This paper explores static solutions in general relativity supported by scalar fields with higher-order potentials, revealing conditions for their existence based on symmetry, field type, and potential form.

## Contribution

It introduces a detailed numerical analysis of regular solutions supported by interacting scalar fields with complex potentials, highlighting the dependence on parameters and symmetry.

## Key findings

- Regular finite energy solutions exist only for specific parameter values.
- Solution existence depends on symmetry, scalar field type, and potential form.
- Numerical methods reveal eigenvalue conditions for solutions.

## Abstract

Domain wall, wormhole, particlelike, and cosmic string general relativistic solutions supported by two interacting phantom or ordinary scalar fields with 4th-, 6th-, and 8th-order potentials are studied. Numerical calculations indicate that regular finite energy solutions exist only for specific values of two free parameters of the potentials. By solving nonlinear eigenvalue problems for some fixed sets of values of the free parameters and of boundary conditions, it is shown that the presence or absence of the solutions depends on a particular symmetry of the problem, on the type of the scalar fields (ordinary or phantom), and on the form of the potential.